We use Curie's law to understand how the magnetism of a paramagnetic material changes with temperature and magnetic field.
According to Curie's law, the magnetisation
(M) is directly proportional to the magnetic field
(B0) and inversely proportional to the temperature
(T) :
M∝ or,
M=C⋅ where
C (Curie's constant) stays the same for the same substance.
Curie's constant can be written as:
C= where:
T= temperature in Kelvin
B0= external magnetic field
M= magnetisation (total dipole moment)
Since
C (Curie's constant) is the same for all measurements of the same sample, we can relate two cases as:
= So,
M2=M1⋅⋅Now, let's fill in the given values:
Number of dipoles
=2×1024Dipole moment per dipole
=15×10−23JT−1Step 1: Find Initial Total Dipole Moment
Total dipole moment possible (if
100% aligned):
2×1024×15×10−23=3×102JT−1 But, at first, only
20% saturation is achieved:
M1=0.2×3×102=60JT−1Step 2: Use Curie's Law for New Conditions
Magnetic field changes from
B01=0.6T to
B02=0.9T and temperature from
T1=4.2K to
T2=2.8K.
Now, use the formula:
M2=M1××Substitute the numbers in:
M2=60××Calculate step by step:
=1.5=1.5So,
M2=60×1.5×1.5=135JT−1
